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Q:

A watch which gains uniformly is 2 minutes low at noon on monday and is 4 min.48 sec fast at 2 p.m on the following monday. when was it correct ?

A) 2 p.m on Tuesday B) 2 p.m on Wednesday
C) 3 p.m on Thursday D) 1 p.m on Friday

Answer:   B) 2 p.m on Wednesday



Explanation:

Time from 12 p.m on monday to 2 p.m on the following monday = 7 days 2 hours = 170 hours

\therefore The watch gains \inline \left ( 2+4\frac{4}{5} \right ) min. or  \inline \frac{34}{5} min. in 170 hrs.

Now, \inline \frac{34}{5} min. are gained in 170 hrs.

\inline \therefore 2 min are gained in \inline \left ( 170\times \frac{5}{34}\times 2 \right ) hrs = 50 hrs

\inline \therefore Watch is correct 2 days 2 hrs. after 12 p.m on monday i.e it will be correct at  2 p.m on wednesday.

Q:

The angle between the minute hand and the hour hand of a clock when the time is 4.15 is

A) 0 B) 37.5
C) 27 D) 15
 
Answer & Explanation Answer: B) 37.5

Explanation:

Angle between hands of a clock

When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock

=>  degrees

Here H = 4, M = 15 and the minute hand is behind the hour hand.

Hence the angle

 = 30[4-(15/5)]+15/2 = 30(1)+7.5 = 37.5 degrees

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6 513
Q:

What is the angle made by the hour hand and the minute hand, if the clock shows 9:15 pm ?

A) 165 degrees B) 172.5 degrees
C) 112.5 degrees D) 125.5 degrees
 
Answer & Explanation Answer: B) 172.5 degrees

Explanation:

The minute hand angle is the easiest since an hour (i.e. 60 minutes) corresponds to the entire 360 degrees, each minute must correspond to 6 degrees. So just multiply the number of minutes in the time by 6 to get the number of degrees for the minute hand.
Here 15 minutes corresponds to 15 x 6 = 90 degrees

Next, you have to figure out the angle of the hour hand. Since there are 12 hours in the entire 360 degrees, each hour corresponds to 30 degrees. But unless the time is EXACTLY something o'clock, you have to write the time as a fractional number of hours rather than as hours and minutes.
Here the time is 9:15 which is (9 + 15/60) = 37/4 hours. Since each hour corresponds to 30 degrees, we multiply 30 to get (37/4)(30) = 277.5 degrees.

Since the hour hand is at 277.5 degrees and the minute hand is at 90 degrees, we can subtract to get the angle of separation. 277.5 - 90 = 187.5 =~ 360 - 187.5 = 172.5 degrees.

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6 924
Q:

How many minutes does a watch lose per day, if its hands coincide every 64 minutes ?

A) 36 7/9 min B) 32 8/11 min
C) 34 3/11 min D) 65 5/11 min
 
Answer & Explanation Answer: B) 32 8/11 min

Explanation:

55 min. spaces are covered in 60 min.

60 min. spaces are covered in open parentheses 60 over 55 cross times 60 close parentheses min. = 65 5 over 11 min.

Loss in 64 min. = open parentheses 65 5 over 11 minus 64 close parentheses equals 16 over 11 min.

Loss in 24 hrs = open parentheses 16 over 11 cross times 1 over 64 cross times 24 cross times 60 close parentheses min. = 32 8 over 11 min.

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5 783
Q:

How many degrees will the minute hand move, in the same time in which the second hand move 4800 ?

A) 80 deg B) 160 deg
C) 140 deg D) 135 deg
 
Answer & Explanation Answer: A) 80 deg

Explanation:

As minute hand covers, 60 degrees

Minute hand covers 4800/60 = 80°

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2 649
Q:

At what time, between 3 o’clock and 4 o’clock, both the hour hand and minute hand coincide each other  ? 

A) 3:16 7/11 B) 3:16 11/4
C) 3:30 D) 3:16 4/11
 
Answer & Explanation Answer: D) 3:16 4/11

Explanation:

Coincide means 00  angle.

This can be calculated using the formulafor time A to B means  [11m/2 - 30 (A)]

Here m gives minutes after A the both hands coincides.

Here A = 3, B = 4

0 =11m/2 –30 × 3
11m = 90 × 2 = 180
m= 180/11 = 16 4/11

So time = 3 : 16 4/11

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3 555